I am also a certified coach and think....
- the stroke is very good for her age
-it might very well develop by itself, spontaneously just by feeding (variation of short balls, deep balls, both backhands and forehands)
-The back swing is however bit too early and straight back and low.

I think it would be better she start with shoulder turn and wait in that position slightly with both hands at racket as long as possible then have the backswing with hand a bit higher (shoulder height), then gravity, pat the dog, and then acceleration through the contact.

If you are playing midsize court keep the present racket or better go to 26 if that is allowed. But when you start with regulation balls and full court play, change to 27 inch racket. I share the view of Rick Macci that 25 inch sticks is more for mini tennis,foam balls and the like.